Curved glass reflections in Glass material
The simulation of refraction depends on light rays being bent twice. Once on the way into the glass, via a front-facing surface, and once on the way out, through a back-facing surface. Your 'good' glass has thickness, so it works. Your 'bad' glass doesn't.
No thickness:

With a Solidify modifier: (No rim. 'Fill' unchecked, so as not to bother with normals interpolating over the rim walls)

If you want a rim on your glass, you will have to bevel it too, to sharpen the interpolation of normals from rim to surface.